2x(3x+4)=1(3x+4)

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Solution for 2x(3x+4)=1(3x+4) equation: 


Simplifying
2x(3x + 4) = 1(3x + 4)

Reorder the terms:
2x(4 + 3x) = 1(3x + 4)
(4 * 2x + 3x * 2x) = 1(3x + 4)
(8x + 6x2) = 1(3x + 4)

Reorder the terms:
8x + 6x2 = 1(4 + 3x)
8x + 6x2 = (4 * 1 + 3x * 1)
8x + 6x2 = (4 + 3x)

Solving
8x + 6x2 = 4 + 3x

Solving for variable 'x'.

Reorder the terms:
-4 + 8x + -3x + 6x2 = 4 + 3x + -4 + -3x

Combine like terms: 8x + -3x = 5x
-4 + 5x + 6x2 = 4 + 3x + -4 + -3x

Reorder the terms:
-4 + 5x + 6x2 = 4 + -4 + 3x + -3x

Combine like terms: 4 + -4 = 0
-4 + 5x + 6x2 = 0 + 3x + -3x
-4 + 5x + 6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-4 + 5x + 6x2 = 0

Factor a trinomial.
(-4 + -3x)(1 + -2x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-1.333333333, 0.5}

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